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A276534 a(n) = a(n-1) * a(n-4) * (a(n-2) * a(n-3) + 1) / a(n-5), with a(0) = a(1) = a(2) = a(3) = a(4) = 1.

%I A276534 #42 Jan 12 2025 04:59:36
%S A276534 1,1,1,1,1,2,4,12,108,10584,27454896,94148851006224,
%T A276534 246222177535609206635748240,
%U A276534 62371770277951054762478578990896212287188931341600,3750595553941161278345366267513070968239986992860645038477600300348697171928615364721752014400
%N A276534 a(n) = a(n-1) * a(n-4) * (a(n-2) * a(n-3) + 1) / a(n-5), with a(0) = a(1) = a(2) = a(3) = a(4) = 1.
%C A276534 Inspired by Somos-5 sequence.
%C A276534 a(n) is an integer for n >= 0.
%C A276534 a(n+1)/a(n) is an integer for n >= 0.
%H A276534 Seiichi Manyama, <a href="/A276534/b276534.txt">Table of n, a(n) for n = 0..17</a>
%F A276534 a(n) * a(n-5) = a(n-1) * a(n-4) + a(n-1) * a(n-2) * a(n-3) * a(n-4).
%F A276534 a(4-n) = a(n).
%F A276534 Let b(n) = b(n-4) * (b(n-2) * (b(0) * b(1) * ... * b(n-3))^2 + 1) with b(0) = b(1) = b(2) = b(3) = 1, then a(n) = a(n-1) * b(n-1) = b(0) * b(1) * ... * b(n-1) for n > 0.
%e A276534 a(5) = a(4) * b(4) =  1 * 2 =   2,
%e A276534 a(6) = a(5) * b(5) =  2 * 2 =   4,
%e A276534 a(7) = a(6) * b(6) =  4 * 3 =  12,
%e A276534 a(8) = a(7) * b(7) = 12 * 9 = 108.
%o A276534 (Ruby)
%o A276534 def A(k, n)
%o A276534   a = Array.new(2 * k + 1, 1)
%o A276534   ary = [1]
%o A276534   while ary.size < n + 1
%o A276534     i = 0
%o A276534     k.downto(1){|j|
%o A276534       i += 1
%o A276534       i *= a[j] * a[-j]
%o A276534     }
%o A276534     break if i % a[0] > 0
%o A276534     a = *a[1..-1], i / a[0]
%o A276534     ary << a[0]
%o A276534   end
%o A276534   ary
%o A276534 end
%o A276534 def A276534(n)
%o A276534   A(2, n)
%o A276534 end
%Y A276534 Cf. A006721, A276535.
%K A276534 nonn
%O A276534 0,6
%A A276534 _Seiichi Manyama_, Nov 16 2016